Thinning

In many applications, the essential shape information of a structure is obtained by representing it with its skeleton made of the medial lines along the main components of the structure. Thinning algorithms produce the skeleton by using criteria that search for the medial lines. The medial axis transform (MAT) [27-29] determines the medial line by computing the distance d(i, j) from each interior pixel i of a binary structure to each boundary pixel j. When the minimal distance of an interior pixel i0 occurs for two boundary pixels jl and j2, min{d(i0, j)} = d(i0 , jl) = d(i0, j2)

has been reported to have low sensitivity to noise as well as the pixel i0 is labeled as an MAT pixel. In some cases, more than two boundary pixels may yield the minimal distance. The result of the MAT depends on the selected distance measure, but typically the Euclidean distance is used. The example shown in Fig. 8a is obtained with the Euclidean distance. The computational complexity of the MAT is high because it requires computation of a large number of distances. Consequently, many iterative algorithms have been developed to determine the medial lines with fewer computations [28,29]. Among